{
  "id": "2505.02458",
  "version": "v1",
  "published": "2025-05-05T08:42:34.000Z",
  "updated": "2025-05-05T08:42:34.000Z",
  "title": "The Quantum Random Energy Model is the Limit of Quantum $ p $-Spin Glasses",
  "authors": [
    "Anouar Kouraich",
    "Chokri Manai",
    "Simone Warzel"
  ],
  "categories": [
    "math-ph",
    "cond-mat.dis-nn",
    "math.MP",
    "math.PR"
  ],
  "abstract": "We consider the free energy of a class of spin glass models with $ p$-spin interactions in a transverse magnetic field. As $ p \\to \\infty $, the infinite system-size free energy is proven to converge to that of the quantum random energy model. This is accomplished by combining existing analytical techniques addressing the non-commutative properties of such quantum glasses, with the description of the typical geometry of extreme negative deviations of the classical $ p $-spin glass. We also review properties of the corresponding classical free energy and conjectures addressing $ 1/p $-corrections in the quantum case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-05-05T08:42:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82D30",
      "82B44"
    ],
    "keywords": [
      "quantum random energy model",
      "existing analytical techniques addressing",
      "infinite system-size free energy",
      "transverse magnetic field",
      "spin glass models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}